This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm...

This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic...

We consider a tree-shaped network of vibrating elastic strings, with feedback acting on the root of the tree. Using the d’Alembert representation formula, we show that the input-output map is bounded, i.e. this system is a well-posed system in the sense of G. Weiss (Trans. Am. Math. Soc. 342 (1994), 827–854). As a consequence we prove that the strings networks are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data.

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain $\Omega$ with control distributed in a subdomain $\omega \subset \Omega \subset {ℝ}^n,n\in \{2,3\}$. The result that we obtained in this paper is as follows. Suppose that $\widehat{v}(t,x)$ is a given solution of the Navier-Stokes equations. Let $v_0\left(x\right)$ be a given initial condition and $\parallel \widehat{v}(0,·)-v_0\parallel \<\epsilon$ where $\epsilon$ is small enough. Then there exists a locally distributed control $u,\text{supp}u\subset (0,T)\times \omega$ such that the solution $v(t,x)$ of the Navier-Stokes equations:$${\partial }_{t}v-\Delta v+(v,\nabla )v=\nabla p+u+f,\text{div}v=0,v{{|}_{\partial \Omega }=0,v|}_{t=0}=v_0$$coincides with...

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain $\omega \subset \Omega \subset {ℝ}^n,n\in \{2,3\}$. The result that we obtained in this paper is as follows. Suppose that $\widehat{v}(t,x)$ is a given solution of the Navier-Stokes equations. Let $v_0\left(x\right)$ be a given initial condition and $\parallel \widehat{v}(0,·)-v_0\parallel <\epsilon$ where ε is small enough. Then there exists a locally distributed control $u,\text{supp}u\subset (0,T)\times \omega$ such that the solution v(t,x) of the Navier-Stokes equations: $${\partial }_{t}v-\Delta v+(v,\nabla )v=\nabla p+u+f,\text{div}v=0,v{{|}_{\partial \Omega }=0,v|}_{t=0}=v_0$$ coincides...

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

Nous quantifions la propriété de continuation unique pour le laplacien dans un domaine borné quand la condition aux bords est a priori inconnue. Nous établissons une estimation de dépen-dance de type logarithmique suivant la terminologie de John [5]. Les outils utilisés reposent sur les inégalités de Carleman et les techniques des travaux de Robbiano [8, 11]. Aussi, nous déterminons en application de l’inégalité d’observabilité obtenue un coût du contrôle approché pour un problème elliptique modèle....

We consider the Laplace equation in a smooth bounded domain. We prove logarithmic estimates, in the sense of John [5] of solutions on a part of the boundary or of the domain without known boundary conditions. These results are established by employing Carleman estimates and techniques that we borrow from the works of Robbiano [8,11]. Also, we establish an estimate on the cost of an approximate control for an elliptic model equation.

The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.

We briefly present the difficulties arising when dealing with the controllability of the discrete wave equation, which are, roughly speaking, created by high-frequency spurious waves which do not travel. It is by now well-understood that such spurious waves can be dealt with by applying some convenient filtering technique. However, the scale of frequency in which we can guarantee that none of these non-traveling waves appears is still unknown in general. Though, using Hautus tests, which read the...

In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.